Can I sell a car with a major fault?

Yes in many cases, but the important question is what the fault does to the executable offer.

Describe the fault accurately

The buyer needs enough information to price the risk.

Prefer real offers over estimates

The as-is value is only useful when somebody is actually prepared to buy at that number.

Compare against repair uplift

Repairing solely to sell is only worthwhile if the sale improvement justifies the cost and risk.

Do not let the sale option bias the decision

PriceYourMotor should show the offer after the independent decision logic, not before.